Question

Let A be as above, consider Ax = b where b = (31, 2, 21, 11). Find x1 using Cramer’s rule. (You may use MATLAB/Octave to compute the determinants, but write out what you are computing.).

Matrix a= 8 6 -3 20

4 2 -5 -7

8 2 7 20

4 2 -11 -4

Answer 1

x1= 1

Explanation:

The Cramer's rule say that x1=
`(det(A1))/(det(A))` where A1 is the matrix A change the column 1 by the vector b.

Then A1=
`\left[\begin{array}{cccc}31&6&-3&20\\2&2&-5&-7\\21&2&7&20\\11& 2&-11&-4\end{array}\right]`.

Using Octave we have that det(A1)=-3840 and det(A)=-3840.

Then x1=
`(-3840)/(-3840)=1`.